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求1X2,2X3,3X4,···49X50的倒数和是多少?怎样列式?

解: (1×2)分之1+(2×3)分之1+(3×4)分之1+……+(49×50)分之1 =(1-2分之1)+(2分之1-3分之1)+(3分之1-4分之1)+……+(49分之1-50分之1) =1-50分之1 =50分之49 结果是50分之49

1/(1*2)+1/(2*3)+1/(3*4)+……+1/(49*50) =1-1/2+1/2-1/3+1/3-1/4+……+1/49-1/50 =1-1/50 =49/50

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